A conceptual DFT study of the molecular properties of glycating carbonyl compounds

Several glycating carbonyl compounds have been studied by resorting to the latest Minnesota family of density functional with the objective of determinating their molecular properties.

RESEARCH ARTICLE

A conceptual DFT study of the molecular

properties of glycating carbonyl compounds

Juan Frau1† and Daniel Glossman‑Mitnik1,2*†

Abstract

Several glycating carbonyl compounds have been studied by resorting to the latest Minnesota family of density func‑ tional with the objective of determinating their molecular properties In particular, the chemical reactivity descriptors that arise from conceptual density functional theory and chemical reactivity theory have been calculated through a

SCF protocol The validity of the KID (Koopmans’ in DFT) procedure has been checked by comparing the reactivity descriptors obtained from the values of the HOMO and LUMO with those calculated through vertical energy values The reactivity sites have been determined by means of the calculation of the Fukui function indices, the condensed

dual descriptor �f (r) and the electrophilic and nucleophilic Parr functions The glycating power of the studied com‑

pounds have been compared with the same property for simple carbohydrates

Keywords: Computational chemistry, Molecular modeling, Glycating carbonyl compounds, Maillard reaction,

Conceptual DFT, Chemical reactivity theory

© The Author(s) 2017 This article is distributed under the terms of the Creative Commons Attribution 4.0 International License ( http://creativecommons.org/licenses/by/4.0/ ), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made The Creative Commons Public Domain Dedication waiver ( http://creativecommons.org/ publicdomain/zero/1.0/ ) applies to the data made available in this article, unless otherwise stated.

Introduction

It is already well known that several diseases like

diabe-tes, Alzheimer and Parkinson are related to the formation

of the so called advanced glycation endproducts (AGEs)

These toxic molecules are the result of a chain of

reac-tions that is initiated by a nucleophilic addition between

a reducing carbonyl compound and the amino groups

of amino acids, peptides, and proteins This is a

nonen-zymatic reaction (nonennonen-zymatic glycation or Maillard

reaction) that leads to the formation of a freely

revers-ible Schiff base Glycated amino acids and proteins can

undergo further reactions, giving rise to the AGEs [1]

Thus, it is very important to understand how the

dif-ferent molecules bearing a reducing carbonyl group

react with the amino acids and proteins and to obtain a

measure of the extent of this reaction in each case The

glycating power, that is, the abilty of different molecules

with reducing carbonyl groups to interact with the amino

group of a proteins is strongly dependent on their molec-ular structures and electronic properties This knowledge could be of interest for the design of new therapeutic drugs and AGEs inhibitors

In a very interesting work, Adrover et  al [2] have studied the kinetics of the interaction of some potential inhibitors of the formation of AGEs with various glycat-ing carbonyl compounds They found that the rate con-stants for the initial reaction between the carbonyl group

of each glycating compound with the amine group of pyridoxamine are strongly dependent on their molecular structures

In a previous work, we have found that the glycation power of simple carbohydrates can be quantified in terms

of the electronic properties of such molecules In par-ticular, it has been proved that good correlations exist between the glycation power and some descriptors that arise from conceptual density functional theory (DFT) This theory, or chemical reactivity theory (as it is also known) is a powerful tool for the prediction, analysis and interpretation of the outcome of chemical reactions [3–6]

From an empirical and practical point of view, it meaningful to follow the procedure of assigning the KS HOMO as equal to and opposite of the vertical ionization

Open Access

*Correspondence: daniel.glossman@cimav.edu.mx

† Juan Frau and Daniel Glossman‑Mitnik contributed equally to this work

2 Departamento de Medio Ambiente y Energía, Laboratorio Virtual

NANOCOSMOS, Centro de Investigación en Materiales Avanzados, Miguel

de Cervantes 120, Complejo Industrial Chihuahua, 31136 Chihuahua,

Chih , Mexico

Full list of author information is available at the end of the article

potential, ǫH = −I and the KS LUMO as equal to and

opposite of the vertical electron affinity, ǫL = −A We

have coined the acronym KID for this empirical

pro-cedure (for “Koopmans in DFT”) This means that how

well a given density functional behaves can be estimated

by checking how well it follows the “Koopmans in DFT”

(KID) procedure and this will be crucial for a good

cal-culation of the Conceptual DFT descriptors that predict

and explain the chemical reactivity of molecular systems

However, we have already observed that this is fulfilled

with varying accuracy for different approximate density

functionals and molecular systems [7–13]

This means that the goodness of a given density

func-tional that allows to predict and explain the chemical

reactivity of a molecular system can be estimated by

checking how well it follows the KID procedure Thus, it

is interesting to study the performance of some new

den-sity functionals that have shown great accuracy across a

broad spectrum of databases in chemistry and physics

[14] on the fulfilling of the KID procedure because only

well-behaved density functionals should be used for the

calculation of molecular properties

The objective of this work is twofold: (i) to conduct a

comparative study of the performance of several of the

latest Minnesota family of density functionals for the

description of the chemical reactivity of some glycating

carbonyl compounds which molecular structures are

shown in Fig. 1; and (ii) to perform a comparison of the

glycation power by relating the experimental rate

con-stants for the initial reaction (or Maillard) of those

mol-ecules with amino groups, with accurately calculated

Conceptual DFT descriptors

Theoretical background

As this work is part of an ongoing project, the theoretical background related to the conceptual DFT global descrip-tors is similar to that presented in previous research and has been already described in detail before [7–13]

For the case of the conceptual DFT local descriptors,

it is worth to mention that the Fukui function is defined

in terms of the derivative of ρ(r) with respect to N and

reflects the ability of a molecular site to accept or donate electrons so two definitions of the Fukui function do exist The first one, f+(r), has been associated to reactiv-ity for a nucleophilic attack so that it measures the

intra-molecular reactivity at the site r towards a nucleophilic

reagent The second one, f−(r), has been associated to reactivity for an electrophilic attack so that this

func-tion measures the intramolecular reactivity at the site r

towards an electrophilic reagent [15]

Morell et al [5 16–21] have proposed a local reactivity descriptor (LRD) which is called the dual descriptor (DD)

f(2)(r) ≡ �f (r) The dual descriptor can be condensed over the atomic sites: when fk>0 the process is driven

by a nucleophilic attack on atom k and then that atom

acts as an electrophilic species; conversely, when fk <0 the process is driven by an electrophilic attack over atom

k and therefore atom k acts as a nucleophilic species.

In 2014, Domingo proposed the nucleophilic and

elec-trophilic Parr functions P(r) [22, 23] as an alternative to the Fukui functions: P−(r) = ρsrc(r) (for electrophilic attacks) and P+(r) = ρsra(r) (for nucleophilic attacks) which are

related to the atomic spin density (ASD) at the r atom of

the radical cation or anion of a given molecule, respectively The ASD over each atom of the radical cation and radical anion of the molecule gives the local nucleophilic P−

k and electrophilic P+

k Parr functions of the neutral molecule [24] Another local reactivity descriptor has been defined so that it permits to measure local reactivities according to the molecular size [18, 19] Such a descriptor is the local hyper-softness (LHS) whose working equation is expressed as

follows: LHS ≈ �f (r) · S2 where S stands for the global

soft-ness [3 25, 26] As the local hypersoftness can be condensed over the atomic sites, the condensed local hypersoftness

is simply computed as LHS ≃ f+

k −fk− · (ǫL− ǫH)−2 The procedure is explained as follows: f(2)

k is expressed in

atomic units, meanwhile S is measured in mili eV raised to

the power of −1, however before performing the multipli-cation, the mili factor is turned back into 10−3 and then S

is raised to the power of 2; the resulting value uses the unit mili eV raised to the power of −2, meaning m (eV−2); the parenthesis is put in order to make clear that the prefix mili

is not raised to the power of −2

Fig 1 Molecular structures of a Acetaldehyde, b Acetol, c Acetone, d

Arabinose, e Glucose, f d‑glyceraldehyde, g Glycoladehyde, h Glyoxal,

i l‑glyceraldehyde, j Methylglyoxal and k Ribose

Setting and computational methods

Following our previous work [7–13], all computational

studies were performed with the Gaussian 09 [27] series

of programs with density functional methods as

imple-mented in the computational package The equilibrium

geometries of the molecules were determined by means

of the gradient technique The force constants and

vibra-tional frequencies were determined by computing

ana-lytical frequencies on the stationary points obtained after

the optimization to check if there were true minima

The basis set used in this work was Def2SVP for

geom-etry optimization and frequencies while Def2TZVP was

considered for the calculation of the electronic properties

[28, 29]

For the calculation of the molecular structure and

properties of the studied systems, we have chosen

sev-eral density functionals from the latest Minnesota density

functionals family, which consistently provide

satisfac-tory results for several structural and thermodynamic

properties [14]: M11, which is a is a range-separated

hybrid meta-GGA [30], M11L, which is a dual-range

local meta-GGA [31], MN12L, which is a nonseparable

local meta-NGA [32], MN12SX, which is a

range-sepa-rated hybrid nonseparable meta-NGA [33], N12, which

is a nonseparable gradient approximation [34], N12SX,

which is a range-separated hybrid nonseparable

gradi-ent approximation [33], SOGGA11, which is a GGA

den-sity functional [35] and SOGGA11X, which is a hybrid

GGA density functional [36] In these functionals, GGA

stands for generalized gradient approximation (in which

the density functional depends on the up and down spin

densities and their reduced gradient) and NGA stands for

nonseparable gradient approximation (in which the

den-sity functional depends on the up/down spin densities

and their reduced gradient, and also adopts a

nonsepa-rable form) All the calculations were performed in the

presence of water as a solvent, by doing IEF-PCM

com-putations according to the SMD solvation model [37]

Results and discussion

Global descriptors

The molecular structures of acetaldehyde, acetol,

ace-tone, arabinose, glucose, d-glyceraldehyde,

glycolade-hyde, glyoxal, l-glyceraldeglycolade-hyde, methylglyoxal, ribose

and N1DDFLT were pre-optimized by starting with the

readily available MOL structures (ChemSpider: http://

www.chemspider.com, PubChem: pubchem.ncbi.nlm

nih.gov), and finding the most stable conformers by

means of the Avogadro 1.2.0 program [38, 39] through a

random sampling with molecular mechanics techniques

and a consideration of all the torsional angles through

the general AMBER force field [40] The structures of

the resulting conformers were then reoptimized with the

eight density functionals mentioned in the previous sec-tion in conjuncsec-tion with the Def2SVP basis set and the SMD solvation model, using water as a solvent

As the validity of the KID procedure could be contro-versial, we have started with the calculation of the con-ceptual DFT global descriptors: global electronegativity

χ, the global hardness η and the global electrophilicity

ω for the studied systems, both through a SCF proce-dure and wlth the values of the orbital energies from the HOMO and LUMO We have extended the calculations

in order to include the electrodonating (ω−) and electro-accepting (ω+) powers as well as the net electrophilicity

�ω± for further verifications

The HOMO and LUMO orbital energies (in eV), ioni-zation potentials I and electron affinities A (in eV), and global electronegativity χ, total hardness η, global elec-trophilicity ω, electrodonating power, (ω−), electroac-cepting power (ω+), and net electrophilicity �ω± of the studied glycating carbonyl compounds calculated with the eight density functionals and the Def2TZVP basis set using water as as solvent simulated with the SMD parametrization of the IEF-PCM model are presented in Additional file 1: Tables S1A–S8A The upper part of the tables shows the results derived assuming the validity of the KID procedure (hence the subscript K) and the lower part shows the results derived from the calculated verti-cal I and A It should be remembered that only the ver-tical energy differences must be included instead of the adiabatic ones, because the Conceptual DFT descriptors

have been defined at a constant external potential v(r).

With the object of analyzing our results and in order

to check for the assessment of the KID procedure, we have previously designed several accuracy descrip-tors (AD) that relate the results obtained through the HOMO and LUMO calculations with those obtained by means of the vertical I and A within a SCF procedure The first three AD are related to the simplest fulfillment

of the KID procedure by relating ǫH with −I, ǫL with

−A, and the behavior of them in the description of the HOMO-LUMO gap: JI = |ǫH+Egs(N − 1) − Egs(N )| ,

JA= |ǫL+Egs(N ) − Egs(N + 1)| and JHL=JI2+JA2 Next, we consider four other descriptors that analyze how well the studied density functionals are useful for the prediction of the electronegativity χ, the global hardness η and the global electrophilicity ω, and for a combination of these Conceptual DFT descriptors, just considering the energies of the HOMO and LUMO or the vertical I and A: Jχ = |χ − χK|, Jη= |η − ηK|, Jω = |ω − ωK| and

JD1=

J2

χ+J2+J2

ω, where D1 stands for the first group

of conceptual DFT descriptors Finally, we designed other four AD to verify the goodness of the studied

density functionals for the prediction of the

electroac-cepting power (ω+), the electrodonating power (ω−), the

net electrophilicity �ω±, and for a combination of these

Conceptual DFT descriptors, just considering the

ener-gies of the HOMO and LUMO or the vertical I and A:

Jω+= |ω+− ω+K|, Jω−= |ω−− ω−K|, J�ω±= |�ω±− �ω±K|

and JD2=

Jω2−+Jω2++J�ω2 ±, where D2 stands for the

second group of Conceptual DFT descriptors

The results of the calculations of JI, JA, JHL, Jχ, Jη, Jω, JD1 ,

Jω+, Jω −, J�ω ± and JD2 for the glycating carbonyl

com-pounds considered in this work are displayed in

Addi-tional file 1: Tables S1B–S8B

On the basis of the results for the descriptors presented

on Additional file 1: Tables S1B–S8B, we have compiled

the average values for for each density functional on the

whole group of glycating carbonyl compounds, and the

calculated results are displayed on Table 1

As can be seen from the results on Table 1, the KID

procedure holds with great accuracy for the MN12SX

and N12SX density functionals, which are

range-sep-arated hybrid meta-NGA and range-seprange-sep-arated hybrid

NGA density functionals, respectively It must be

stressed that it was not our intention to perform a

gap-fitting by minimizing a descriptor by choosing an

opti-mal range-separation parameter, but to check if the

density functionals considered in this study fulfill the

KID procedure Indeed, the values of JI, JA and JHL are

not exactly zero However, their values can be favorably

compared with the results presented for these

quanti-ties in the work of Lima et  al [41], where the minima

has been obtained by choosing a parameter that enforces

that behavior

It is interesting to see that the same density

function-als function-also fulfill the KID procedure for the other

descrip-tors, namely Jχ, Jη, Jω, and JD1, as well as for Jω −, Jω +, J�ω ± ,

and JD2 These results are very important, because they

show that it is not enough to rely only in JI, JA and JHL For example, if we consider only Jχ, for all of the density func-tionals considered, the values are very close to zero As for the other descriptors, only the MN12SX and N12SX density functionals show this behavior That means that the results for Jχ are due to a fortuitous cancellation of errors

The usual GGA (SOGGA11) and hybrid-GGA (SOG-GA11X) are not good for the fulfillment of the KID pro-cedure, and the same conclusion is valid for the local functionals M11L, MN12L and N12 An important fact

is that although the range-separated hybrid NGA and range-separated hybrid meta-NGA density functionals can be useful for the calculation of the conceptual DFT descriptors, it is not the same for the range-separated hybrid GGA (M11) density functional An inspection

of Additional file 1: Table S1A shows that this is due to the fact that this functional describes inadequately the energy of the LUMO, leading to positive values of A (with the exception of glyoxal and methylglyoxal), which are in contradiction with the SCF results

Local descriptors

The condensed Fukui functions can also be employed to determine the reactivity of each atom in the molecule and have been calculated using the AOMix molecular analy-sis program [42, 43] starting from single-point energy calculations, while the condensed dual descriptor was calculated as fk=f+k −f−k [16, 17] From the interpre-tation given to the Fukui function, one can note that the sign of the dual descriptor is very important to charac-terize the reactivity of a site within a molecule towards a nucleophilic or an electrophilic attack That is, if �fk >0, then the site is favored for a nucleophilic attack, whereas

if �fk <0, then the site may be favored for an electro-philic attack [16, 17, 44] These results may be compared with the values of the electrophilic Parr function over the

Table 1 Average descriptors JI, JA, JHL, Jχ, Jη, Jω, J D1 , Jω +, Jω −, J�ω± and J D2  for the acetaldehyde, acetol, acetone, arabinose, glucose, d -glyceraldehyde, glycolaldehyde, glyoxal, l -glyceraldehyde, methylglyoxal and  ribose molecules calculated with  the M11, M11L, MN12L, MN12SX, N12, N12SX, SOGGA11 and  SOGGA11X density functionals and  the Def2TZVP basis set using water as as solvent simulated with the SMD parametrization of the IEF-PCM model

carbonyl C atoms of the studied compounds by means of

the ASD of the corresponding radical anion

The condensed Fukui functions, the condensed dual

descriptor fk and the electrophilic P+

k Parr functions over the carbonyl C atoms of the acetaldehyde, acetol,

acetone, arabinose, glucose, d-glyceraldehyde,

glycolade-hyde, glyoxal, l-glyceraldeglycolade-hyde, methylglyoxal and ribose

molecules calculated with the MN12SX and N12SX

den-sity functionals and the Def2TZVP basis set using water

as as solvent simulated with the SMD parametrization of

the IEF-PCM model are shown in Table 2 For the

calcu-lation of the ASD, we have considered both a Mulliken

Population Analysis (MPA) [45–48] or a Hirshfeld

Popu-lation Analysis (HSA) [49–51] modified to render CM5

atomic charges [52]

Glycating power

In a previous work [53], we have studied the glycating

power (GP) of simple carbohydrates and tried to explain

it in terms of the calculated conceptual DFT descriptors

To this end, we performed a Linear Regression Analysis

(LRA) of the results of plotting the rate of condensation

of monosaccharides with pyridoxamine (k3) [54] against

the global electrophilicity ω A good relationship between

the glycating power (GP) and the global

electrophilic-ity ω was obtained for the model chemistry MN12SX/

Def2TZVP/SMD(H2O), according to the following

equa-tion: GP = a × ω + b, where GP = k3, a is the slope and b

is the interception of the linear correlation The values of

a and b were 87.5200 and −134.3312 respectively, giving

rise to a MAD of 0.5840

It could be interesting to perform a similar analysis for the glycating carbonyl compounds studied in this work starting from the values for the rate constants k1 com-piled by Adrover et  al [2] The experimental values of

k1 (in M−1 h−1) (taken from the mentioned work [2]) are reproduced here for the sake of convenience: Acetone = 3.9 × 101, Acetol = 8.5 × 101, Acetaldehyde = 3.0 × 104, Glycolaldehyde = 2.2 × 105, Glucose = 3.7 × 105, Ribose

= 3.9 × 105, Arabinose = 2.9 × 105, Glyoxal = 1.8 × 107, Methylglyoxal = 1.1 × 106 However, this is not an easy task because the k1 values for glyoxal and methylglyoxal are one or two orders of magnitude larger than for the other aldehydes (including aldoses) and several orders of magnitude larger than the ketones (acetol and acetone) This makes impossible to span accurately all the values within a LRA

However, a qualitative trend may be observed in terms

of the global electrophilicty ω An inspection of Addi-tional file 1: Tables S4A–S6A of the ESI reveals that for MN12SX and N12SX density functionals, the results for glyoxal and methylglyoxal are larger than for the other molecules considered in this work, in agreement with the experimental results [2] In turn, the values for acetol and acetone are the smallest ones, again in a good agreement with the experiments

One could also expect that a similar trend could be obtained from the local descriptors presented in Table 2

Indeed, this is not case for the electrophilic Fukui func-tion f+

k and the condensed dual descriptor  fk because the are sub-intensive properties Now paying attention to the electrophilic Parr functions P+

k(mpa) and P+

k(hpa), it

Table 2 Electrophilic Fukui functions, condensed dual descriptors and  electrophilic Parr functions for  the acetalde-hyde, acetol, acetone, arabinose, glucose, d -glyceraldehyde, glyoxal, glycolaldehyde, l -glyceraldehyde, methylglyoxal and ribose molecules calculated with the MN12SX and N12SX density functionals and the Def2TZVP basis set using water

as as solvent simulated with the SMD parametrization of the IEF-PCM model

MPA Mulliken population analysis, HPA Hirshfeld population analysis

f+k f k P+k (mpa) P+k (hpa) f+k f k P+k (mpa) P+k (hpa)

can be observed that there are no significative differences

for the results in the first case, while the second

pre-dicts lower values for acetol and acetone, as it should be

expected However, this method fails to predict greater

values for glyoxal and methylglyoxal

It is worth to look at the results for d- and

l-glyceralde-hyde because they were not included in the experimental

work of Adrover et al [2] Our calculations predict that

the glycating power GP of both molecules will be slighty

lower than the value for glucose

The condensed local hypersoftness (LHS) over the

car-bonyl C atoms of the acetaldehyde, acetol, acetone,

arab-inose, glucose, d-glyceraldehyde, glycoladehyde, glyoxal,

l-glyceraldehyde, methylglyoxal and ribose molecules

calculated with the MN12SX and N12SX density

func-tionals and the Def2TZVP basis set using water as as

solvent simulated with the SMD parametrization of the

IEF-PCM model are shown in Table 3

The results are noteworthy If we take the LHS as a

measure of the glycating power GP, it can be observed

that for the MN12SX and N12SX density functionals, the

values for glyoxal and methylglyoxal almost double those

for the ketones (acetol and acetone) The other

alde-hydes (including the aldoses) display intermediate

val-ues This is in agreement with the experimental results

Notwithstanding, there is a small discrepancy between

both functionals While MN12SX predicts that the GP of

methylglyoxal will be (slighty) larger than that of glyoxal,

only the second, N12SX, shows the correct trend, that is,

GP (glyoxal) > GP (methylglyoxal)

Conclusions

The Minnesota family of density functionals (M11, M11L, MN12L, MN12SX, N12, N12SX, SOGGA11 and SOG-GA11X) have been tested for the fulfillment of the KID procedure by comparison of the HOMO- and LUMO-derived values with those obtained through a SCF procedure It has been shown that the range-separated hybrid meta-NGA density functional (MN12SX) and the range-separated hybrid NGA density functional (N12SX) are the best for the accomplishment of this objective As such, they represent a good prospect for their usefulness

in the description of the chemical reactivity of molecular systems of large size

From the whole of the results presented in this work,

it can be seen that the sites of interaction of the glyca-tiong carbonyl compounds can be predicted by using DFT-based reactivity descriptors such as the elec-tronegativity, global hardness, global electrophilic-ity, electrodonating and electroaccepting powers, net electrophilicity as well as Fukui function, condensed dual descriptor and condensed local hypersoftness cal-culations These descriptors were used in the charac-terization and successfully description of the preferred reactive sites and provide a firm explanation for the reactivity of those molecules

Moreover, the difference in the glycating power GP between aldehydes and ketones could be explained in terms of the conceptual DFT descriptors This is based

on calculations performed with the MN12SX density functional in conexion with the Def2TZVP basis set and the SMD parametrization of the IEF-PCM model using water as a solvent It can be concluded that this model chemistry [MN12SX/Def2TZVP/SMD (Water)] is the best for fulfilling the KID procedure and for the pre-diction of the glycating power GP of the carbonyl com-pounds and could be used for the study of the behavior

of larger molecules bearing carbonyl C atoms capable of taking part in the Maillard reaction

Authors’ contributions

DGM conceived and designed the research and headed, wrote and revised the manuscript, while JF contributed to the writing and the revision of the article Both authors read and approved the final manuscript.

Author details

1 Departament de Química, Universitat de les Illes Balears, Carretera de Vall‑ demossa, Km 7.5, 07010 Palma, Spain 2 Departamento de Medio Ambiente y Energía, Laboratorio Virtual NANOCOSMOS, Centro de Investigación en Mate‑ riales Avanzados, Miguel de Cervantes 120, Complejo Industrial Chihuahua,

31136 Chihuahua, Chih , Mexico

Additional file

Additional file 1. Additional tables.

Table 3 Condensed local hypersoftness (LHS) over the

car-bonyl C atoms of the acetaldehyde, acetol, acetone,

arab-inose, glucose, d -glyceraldehyde, glyoxal, glycolaldehyde,

l -glyceraldehyde, methylglyoxal and  ribose molecules

calculated with the M06 and MN12SX density functionals

and the Def2TZVP basis set using water as as solvent

simu-lated with the SMD parametrization of the IEF-PCM model

This work has been partially supported by CIMAV, SC and Consejo Nacional

de Ciencia y Tecnología (CONACYT, Mexico) through Grant 219566/2014 for

Basic Science Research and Grant 265217/2016 for a Foreign Sabbatical Leave

DGM conducted this work while a Sabbatical Fellow at the University of the

Balearic Islands from which support is gratefully acknowledged This work was

cofunded by the Ministerio de Economía y Competitividad (MINECO) and the

European Fund for Regional Development (FEDER) (CTQ2014‑55835‑R).

Competing interests

The authors declare that they have no competing interests.

Received: 15 December 2016 Accepted: 9 January 2017

References

1 Ahmed N (2005) Advanced glycation endproducts—role in pathology of

diabetic complications Diabetes Res Clin Pract 67:3–21

2 Adrover M, Vilanova B, Frau J, Muñoz F, Donoso J (2009) A comparative

study of the chemical reactivity of pyridoxamine, Ac‑Phe‑Lys and Ac‑Cys

with various glycating carbonyl compounds Amino Acids 36:437–448

3 Parr RG, Yang W (1989) Density‑functional theory of atoms and mol‑

ecules Oxford University Press, New York

4 Geerlings P, De Proft F, Langenaeker W (2003) Conceptual density func‑

tional theory Chem Rev 103:1793–1873

5 Toro‑Labbé A (ed) (2007) Theoretical aspects of chemical reactivity, vol

19 Elsevier Science, Amsterdam

6 Chattaraj PK (ed) (2009) Chemical reactivity theory—a density functional

view CRC Press, Boca Raton

7 Glossman‑Mitnik D (2013) A comparison of the chemical reactivity of

naringenin calculated with M06 family of density functionals Chem Cent

J 7:155–161

8 Martínez‑Araya JI, Salgado‑Morán G, Glossman‑Mitnik D (2013) Compu‑

tational nanochemistry report on the oxicams—conceptual DFT and

chemical reactivity J Phys Chem B 117(21):6639–6651

9 Glossman‑Mitnik D (2013) Computational nanochemistry study of the

chemical reactivity properties of the rhodamine B molecule Procedia

Comput Sci 18:816–825

10 Martínez‑Araya JI, Salgado‑Morán G, Glossman‑Mitnik D (2013)

Computational nutraceutics: chemical reactivity properties of the

flavonoid naringin by means of conceptual DFT J Chem 2013:850297

doi: 10.1155/2013/850297

11 Glossman‑Mitnik D (2014) Chemical reactivity theory within DFT applied

to the study of the prunin flavonoid Eur Int J Sci Technol 3(9):195–207

12 Glossman‑Mitnik D (2014) Computational chemistry of natural products:

a comparison of the chemical reactivity of isonaringin calculated with the

M06 family of density functionals J Mol Model 20(2316):1–7

13 Frau J, Muñoz F, Glossman‑Mitnik D (2016) A molecular electron density

theory study of the chemical reactivity of cis‑ and trans‑resveratrol Mol‑

ecules 21(12):1650

14 Peverati R, Truhlar DG (2014) Quest for a universal density functional: the

accuracy of density functionals across a broad spectrum of databases in

chemistry and physics Phil Trans R Soc Lond 372(2011):20120476

15 Parr RG, Yang W (1984) Density functional approach to the Frontier‑

electron theory of chemical reactivity J Am Chem Soc 106:4049–4050

16 Morell C, Grand A, Toro‑Labbé A (2005) New dual descriptor for chemical

reactivity J Phys Chem A 109:205–212

17 Morell C, Grand A, Toro‑Labbé A (2006) Theoretical support for using the

�f (r) descriptor Chem Phys Lett 425:342–346

18 Cárdenas C, Rabi N, Ayers PW, Morell C, Jaramillo P, Fuentealba P (2009)

Chemical reactivity descriptors for ambiphilic reagents: dual descriptor, local

hypersoftness, and electrostatic potential J Phys Chem A 113:8660–8667

19 Ayers PW, Morell C, De Proft F, Geerlings P (2007) Understanding the

Woodward–Hoffmann rules by using changes in electron density Chem

Eur J 13:8240–8247

20 Morell C, Ayers PW, Grand A, Gutiérrez‑Oliva S, Toro‑Labbé A (2008)

Rationalization of the Diels–Alder reactions through the use of the dual

reactivity descriptor �f (r) Phys Chem Chem Phys 10:7239–7246

21 Morell C, Hocquet A, Grand A, Jamart‑Grégoire B (2008) A conceptual DFT study of hydrazino peptides: assessment of the nucleophilicity of

the nitrogen atoms by means of the dual descriptor �f (r) J Mol Struct

THEOCHEM 849:46–51

22 Domingo LR, Pérez P, Sáez JA (2013) Understanding the local reactivity in polar organic reactions through electrophilic and nucleophilic Parr func‑ tions RSC Adv 3:1486–1494

23 Chamorro E, Pérez P, Domingo LR (2013) On the nature of Parr functions

to predict the most reactive sites along organic polar reactions Chem Phys Lett 582:141–143

24 Domingo LR, Ríos‑Gutiérrez M, Pérez P (2016) Applications of the con‑ ceptual density functional theory indices to organic chemistry reactivity Molecules 21:748

25 Pearson RG (1993) The principle of maximum hardness Acc Chem Res 26:250–255

26 Chermette H (1999) Chemical reactivity indexes in density functional theory J Comput Chem 20:129–154

27 Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato

M, Li X, Hratchian HP, Izmaylov AF, Bloino J, Zheng G, Sonnenberg JL, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery JA Jr, Peralta JE, Ogliaro

F, Bearpark M, Heyd JJ, Brothers E, Kudin KN, Staroverov VN, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant JC, Iyengar SS, Tomasi J, Cossi M, Rega N, Millam JM, Klene M, Knox JE, Cross JB, Bakken V, Adamo

C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Martin RL, Morokuma K, Zakrzewski VG, Voth GA, Salvador P, Dannenberg JJ, Dapprich S, Daniels AD, Farkas O, Foresman JB, Ortiz JV, Cioslowski J, Fox DJ (2009) Gaussian 09 Revision D.01 Gaussian Inc., Wallingford

28 Weigend F, Ahlrichs R (2005) Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: design and assessment of accuracy Phys Chem Chem Phys 7:3297–3305

29 Weigend F (2006) Accurate Coulomb‑fitting basis sets for H to R Phys Chem Chem Phys 8:1057–1065

30 Peverati R, Truhlar DG (2011) Improving the accuracy of hybrid meta‑GGA density functionals by range separation J Phys Chem Lett 2(21):2810–2817

31 Peverati R, Truhlar DG (2012) M11‑L: a local density functional that provides improved accuracy for electronic structure calculations in chemistry and physics J Phys Chem Lett 3(1):117–124

32 Peverati R, Truhlar DG (2012) An improved and broadly accurate local approximation to the exchange‑correlation density functional: the MN12‑L functional for electronic structure calculations in chemistry and physics Phys Chem Chem Phys 14(38):13171–13174

33 Peverati R, Truhlar DG (2012) Screened‑exchange density functionals with broad accuracy for chemistry and solid‑state physics Phys Chem Chem Phys 14(47):16187–16191

34 Peverati R, Truhlar DG (2012) Exchange‑correlation functional with good accuracy for both structural and energetic properties while depend‑ ing only on the density and its gradient J Chem Theory Comput 8(7):2310–2319

35 Peverati R, Zhao Y, Truhlar DG (2011) Generalized gradient approximation that recovers the second‑order density‑gradient expansion with opti‑ mized across‑the‑board performance J Phys Chem Lett 2(16):1991–1997

36 Peverati R, Truhlar DG (2011) Communication: a global hybrid general‑ ized gradient approximation to the exchange‑correlation functional that satisfies the second‑order density‑gradient constraint and has broad applicability in chemistry J Chem Phys 135(19):191102

37 Marenich A, Cramer C, Truhlar D (2009) Universal solvation model based

on solute electron density and a continuum model of the solvent defined by the bulk dielectric constant and atomic surface tensions J Phys Chem B 113:6378–6396

38 Avogadro: an open‑source molecular builder and visualization tool Ver‑ sion 1.2.0 (2016) http://avogadro.openmolecules.net

39 Hanweel MD, Curtis DE, Lonie DC, Vandermeersch T, Zurek E, Hutchison

GR (2012) Avogadro: an advanced semantic chemical editor, visualization, and analysis platform J Cheminform 4:17

40 Wang J, Wolf RM, Caldwell JW, Kollman PA, Case DA (2004) Develop‑ ment and testing of a general AMBER force field J Comput Chem 25(9):1157–1174

41 Lima IT, Prado ADS, Martins JBL, de Oliveira Neto PH, Ceschin AM, da Silva

Filho DA (2016) Improving the description of the optical properties of

carotenoids by tuning the long‑range corrected functionals J Phys Chem

A 120(27):4944–4950

42 Gorelsky SI (2011) AOMix program for molecular orbital analysis—version

6.5 University of Ottawa, Ottawa

43 Gorelsky SI, Lever ABP (2001) Electronic structure and spectra of

ruthenium diimine complexes by density functional theory and INDO/S

Comparison of the two methods J Organomet Chem 635(1–2):187–196

44 Gázquez JL (2009) Chemical reactivity concepts in density functional

theory In: Chattaraj PK (ed) Chemical reactivity theory: a density func‑

tional view CRC Press, Boca Raton, pp 7–21

45 Lewars E (2003) Computational chemistry—introduction to the theory

and applications of molecular and quantum mechanics Kluwer Aca‑

demic Publishers, Dordrecht

46 Young DC (2001) Computational chemistry—a practical guide for apply‑

ing techniques to real‑world problems Wiley, New York

47 Jensen F (2007) Introduction to computational chemistry, 2nd edn Wiley,

Chichester

48 Cramer CJ (2004) Essentials of computational chemistry—theories and models, 2nd edn Wiley, Chichester

49 Hirshfeld FL (1977) Bonded‑atom fragments for describing molecular charge densities Theor Chimica Acta 44(2):129–138

50 Ritchie JP (1985) Electron density distribution analysis for nitromethane, nitromethide, and nitramide J Am Chem Soc 107:1829–1837

51 Ritchie JP, Bachrach SM (1987) Some methods and applications of elec‑ tron density distribution analysis J Comput Chem 8:499–509

52 Marenich AV, Jerome SV, Cramer CJ, Truhlar DG (2012) Charge model 5: an extension of hirshfeld population analysis for the accurate description of molecular Interactions in gaseous and condensed phases J Chem Theory Comput 8:527

53 Frau J, Glossman‑Mitnik D A comparative study of the glycating power

of simple carbohydrates in the Maillard reaction by means of conceptual DFT descriptors J Mol Gr Model (submitted)

54 Adrover M, Vilanova B, Muñoz F, Donoso J (2007) Pyridoxamine, a scaven‑ ger agent of carbohydrates Int J Chem Kinet 39(3):154–167